mathematics

R. L. Hudson

R. L. Hudson is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand R. L. Hudson rather than just read about it. In short: Robin Lyth Hudson (4 May 1940 – 12 January 2021) was a British mathematician notable for his contribution to quantum probability. Education and career Hudson received his Ph.D. from the University of Oxford in 1966 under John T.

Key takeaways

R. L. Hudson belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect R. L. Hudson to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of R. L. Hudson from memory before moving on to harder problems.

Reference excerpt

Robin Lyth Hudson (4 May 1940 – 12 January 2021) was a British mathematician notable for his contribution to quantum probability.

Education and career Hudson received his Ph.D. from the University of Oxford in 1966 under John T. Lewis with a thesis entitled Generalised Translation-Invariant Mechanics. He was appointed assistant lecturer at the University of Nottingham in 1964, promoted to a chair in 1985 and served as head of department from 1987 to 1990. He spent sabbatical semesters in Heidelberg (1978), Austin, Texas (1983), and Colorado Boulder (1996). After taking early retirement in 1997, he held part-time research posts at Nottingham Trent University (1997–2005), the Slovak Academy of Sciences (1997–2000) and Loughborough University (2005–21), and a visiting professorship at the University of Łódź (2002) which awarded him an honorary doctorate in 2013. Hudson was a mathematical physicist who was one of the pioneers of quantum probability. An early result, now known as Hudson's theorem in quantum optics, shows that the pure quantum states with positive Wigner quasiprobability distribution are the Gaussian ones. Together with PhD students, Hudson established one of the first quantum central limit theorems, proved an early quantum de Finetti theorem, and introduced quantum Brownian motion as a non-commuting pair of families of unbounded operators, using the formalism of quantum field theory. He collaborated with K. R. Parthasarathy first at the University of Manchester, and later at University of Nottingham and at Loughborough University, on their seminal work in quantum stochastic calculus. In later papers he developed a theory of quantum stochastic double product integrals and their application to the quantum Yang–Baxter equation, the quantisation of Lie bialgebras and quantum Lévy area.

Selected works Hudson, R. L.; Ion, P. D. F.; K. R. Parthasarathy (1982). "Time-orthogonal unitary dilations and non-commutative Feynman-Kac formulae". Communications in Mathematical Physics. 83 (2): 261–280. Bibcode:1982CMaPh..83..261H. doi:10.1007/BF01976044. hdl:2027.42/46525. Hudson, R. L.; K. R. Parthasarathy (1984). "Quantum Ito's formula and stochastic evolutions". Communications in Mathematical Physics. 93 (3): 301–323. Bibcode:1984CMaPh..93..301H. doi:10.1007/bf01258530. S2CID 122848524. Archived from the original on 28 October 2015. Hudson, R. L.; K. R. Parthasarathy (1984). "Stochastic dilations of uniformly continuous completely positive semigroups". Acta Applicandae Mathematicae. 2 (3–4): 353–378. doi:10.1007/BF02280859. S2CID 189915711. Applebaum, D. B.; Hudson, R. L. (1984). "Fermion Ito's formula and stochastic evolutions". Communications in Mathematical Physics. 96 (4): 473–496. doi:10.1007/BF01212531. S2CID 120125103. Hudson, R. L.; Lindsay, J. M. (1985). "A non-commutative martingale representation theorem for non-Fock quantum Brownian motion". Journal of Functional Analysis. 61 (2): 202–221. doi:10.1016/0022-1236(85)90034-5. Hudson, R. L.; K. R. Parthasarathy (1986). "Unification of Boson and Fermion quantum stochastic calculus". Communications in Mathematical Physics. 104 (3): 457–470. Bibcode:1986CMaPh.104..457H. doi:10.1007/BF01210951. S2CID 123132851. Hudson, R. L.; K. R. Parthasarathy (1994). "Casimir chaos in a Boson Fock space". Journal of Functional Analysis. 119 (2): 319–339. doi:10.1006/jfan.1994.1013. Hudson, R. L.; Pulmannová, S. (2004). "Double product integrals and Enriquez quantisation of Lie bialgebras I: The quasitriangularity relations". Journal of Mathematical Physics. 45: 2090–2105. doi:10.1063/1.1649796.

References

External links Mathematical genealogy project page on Robin Lyth Hudson Hudson ancestry

Illustrations

Worked examples

Example 1 — a first encounter with R. L. Hudson

Start with the simplest possible case. Write down what R. L. Hudson claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to R. L. Hudson before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about R. L. Hudson ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of R. L. Hudson

In research: R. L. Hudson appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses R. L. Hudson in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: R. L. Hudson is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1940 births, 20th-century British mathematicians, 21st-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for R. L. Hudson outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study R. L. Hudson in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what R. L. Hudson means in your own words.
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Frequently asked questions

What is R. L. Hudson in simple terms?

Robin Lyth Hudson (4 May 1940 – 12 January 2021) was a British mathematician notable for his contribution to quantum probability. Education and career Hudson received his Ph.D. from the University of Oxford in 1966 under John T.

Why does R. L. Hudson matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study R. L. Hudson?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on R. L. Hudson.